Adaptive modulation interval filtering algorithm based on empirical mode decomposition

Accepted Manuscript Adaptive Modulation Interval Filtering Algorithm Based on Empirical Mode Decomposition Xinyu Dao, Min Gao, Chaowang Li PII: DOI: Reference:

S0263-2241(19)30364-1 https://doi.org/10.1016/j.measurement.2019.04.046 MEASUR 6561

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

6 December 2018 28 February 2019 12 April 2019

Please cite this article as: X. Dao, M. Gao, C. Li, Adaptive Modulation Interval Filtering Algorithm Based on Empirical Mode Decomposition, Measurement (2019), doi: https://doi.org/10.1016/j.measurement.2019.04.046

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1 

Adaptive Modulation Interval Filtering Algorithm Based on Empirical Mode Decomposition Xinyu Dao, Min Gao and Chaowang Li

Xinyu Dao: Army Engineering University, Shijiazhuang, China. Min Gao: Army Engineering University, Shijiazhuang, China. Chaowang Li: Army Engineering University, Shijiazhuang, China. Abstract—To improve the denoising performance of echo signal in a receiver of frequency modulated system, an adaptive modulation interval threshold denoising algorithm on the basis of empirical mode decomposition is proposed. By means of measuring the energy variation in each intrinsic mode function of noise interference and different background clutter, the optimal decomposition stopping time of empirical mode decomposition and the order of intrinsic mode functions needed to be filtered are determined. Combined with the soft interval threshold, an adjustment factor is added into the soft interval threshold formula to process the intrinsic mode function adaptively. The simulation and practical measurement results show that the proposed method improves signal-to-noise ratio by 1-3dB and reduces the root mean square error by 10-25% compared with the direct empirical mode decomposition denoising method and traditional threshold denoising method. Index Terms—Empirical mode decomposition, Interval threshold denoising, Information extraction, frequency modulated system.

I. INTRODUCTION

I

N FREQUENCY modulated system, the echo signal received by the receiver usually contains a lot of clutter and noise generated by the system itself. Whether these interferences could be effectively suppressed or eliminated is the key to achieve accurate ranging measurement. Therefore, it is essential to find effective methods to filter out the interferences. Empirical mode decomposition (EMD), a method applied to nonlinear and non-stationary random signal processing and analysis, is gradually developed due to great adaptability [1-5]. This method can decompose the complex signal into a series of intrinsic mode functions (IMF) with frequency decreasing

sequence according to its own characteristics [6-8]. Wang Y.H. proved that EMD algorithm has the same computational cost as Fourier transform for the first time [9], which provided a theoretical basis for EMD to process echo signal in frequency modulated system. However, in the process of EMD, the suitable stopping criterion directly affects the timeliness of signal processing. Huang et al. put forward the criterion of standard deviation to determine the time of decomposition stopping, which provides a good idea in general sense whereas it is not necessary to completely decompose when using the criterion in some practical measurement environment. The noise, clutter and target signal in the echo signal are arranged in every IMF components after EMD. In order to effectively remove the noise and clutter interference in the echo signal, we should study the variation characteristics of noise and clutter in each order of IMF components. When the interference in IMF component has little effect on the target signal, it is not necessary to continue to decompose the signal. The frequency spectrum of each IMF component has its corresponding central frequency while it will be widened or submerged by interference. It is difficult to extract useful information from the perspective of spectrum analysis alone. The [10] pointed out that the energy spectrum of the IMF component can better reflect the IMF energy variety of different signal types. Therefore, based on the above analysis, the characteristics of noise and clutter energy changing with decomposition layers in the echo signal are researched to determine the EMD stopping time so that unnecessary decomposition could be avoided. For the decomposed IMF components, there are two pervasive methods to filter. One is to directly remove the high-order IMF components and then reconstruct the remaining items to obtain effective information. It inevitably removes the useful information contained in the high-order IMF components at the same time. Another is to set a threshold to process IMF components. Nevertheless, the same threshold commonly used for different IMFs causes the signal information obliteration or redundancy. Thus, a method of modulation interval threshold filtering for different order intrinsic mode functions is proposed. By introducing adjustment factor into traditional soft threshold formula to reduce the distortion caused by excessive amplitude in interval threshold processing, the original characteristics of the signal are retained as much as possible and the filtering performance is further improved. The structure of this paper is arranged as follows. The second part briefly introduces the basic principle of EMD. The third part focuses on the analysis of the energy variation of different IMFs of noise and different background environments clutter. The appropriate decomposition stopping time is also determined. The main algorithm of modulation interval filtering proposed in this paper is described in the fourth part. The corresponding simulation and practical verification are presented in the fifth part. The last part summarizes the full paper. II. BASIS OF EMD EMD is a time-frequency analysis approach that adaptively

2 decomposes a signal into a series of intrinsic mode functions permuted in the descending order of frequency. The IMF must satisfy two conditions[11]: (1) zero-crossing condition, namely the number of extrema(including maximum and minimum) and zero-crossings are required to be equal or differ by one at most. (2) mean condition, it means that the mean value of the envelope constructed by the local maximum and local minimum is zero at any point. The EMD is a total data processing method based on the local characteristics of timescale, which the basis function or the parameters of filters are not determined in advance. Therefore, the instantaneous frequency obtained by EMD possess a strong physical meaning. The sifting process is described as Table.1

s(t ) ,namely

white noise in each order of the IMF component was given as the following. 2   median( hi (t ) )   Ei    ,i  1  0.6745   (2)  E1  i   Ei    , i  2,3,..., n  Where, Ei reprents the energy of the i-th order IMF. The parameters  and  are the constant, which are usually set to be 0.719 and 2.01 respectively to ensure that the noise energy can be reduced linearly in the logarithmic form [13,14]. Actually, compared with the conclusion given by Wu Z., we are more concerned about the variation of white noise with decomposition layers rather than the estimated value. In order to observe the energy change characteristics of white noise in each order IMF more intuitively, a Gaussian white noise is generated randomly in Matlab software. The noise length is set to 1000. Only the Gaussian white noise is decomposed by EMD, and the energy magnitude Ei of each order IMF component is calculated by the formula (3). 2 (3) Ei   hi (t ) dt , i  1, 2,3,...

m1 (t ) :

The decomposition results are shown in Fig. 1 and the corresponding energy variation is presented in Fig. 2 after normalizing the calculated energy.

Table 1 Sifting process of EMD Algorithm：Sifting process of EMD Step1：Find out all local maximum and local minimum value of the original signal s(t ) Step2： Form the upper envelope eu (t ) and lower envelope ed (t ) using the cubic spline interpolation curve constructed by the local maximum and minimum of s(t ) respectively Step3 ： Calculate

the

local

mean

m1 (t ) of the

m1 (t )  (eu (t )  ed (t )) / 2 Step4 ： Calculate

the

difference

between

s(t )

and

h1 (t )  s(t )  m1 (t )

Step7 ： If the r1 (t ) is either monotonous or a constant, terminate the

III. DETERMINATION OF DECOMPOSITION STOP TIME The echo signal in frequency modulated system contains noise and clutter caused by different background environment. According to the energy variation characteristics of noise and clutter in each order of IMF, the appropriate time of EMD decomposition stopping is determined. A. Energy variation characteristics of noise in echo signal The main source of noise in the echo signal is the internal noise generated by the receiver itself, which exists in the form of high-level amplifier. Therefore, it can be considered as Gauss white noise. Wu Z. et al. [12] used EMD to study white noise. It was found that the multiplication of energy density and average period in each order of IMF decomposed by white noise was constant. At the same time, the energy estimation of

-1

IMF4 IMF5 IMF6 IMF7

where hi (t ) represents the IMF, rn (t ) is the residual component.

r

(1)

i 1

-2 1 0 -1 1 0 -1 0.5 0 -0.5 0.5 0 -0.5 1 0

Amplitude

n

s(t )   hi (t )  rn (t )

IMF3

-2 2 0

decomposition. If not, repeat Step1~Step5

After decomposing, the original signal can be expressed as follows:

IMF2

Step6 ：After obtaining the first IMF h1 (t ) , calculate the residue r1 (t ) :

r1 (t )  s(t )  h1 (t )

IMF1

5 0 -5 2 0

Step5：Repeat Step1~Step4 until h1 (t ) satisfy the conditions of IMF

0

200

400 600 Samples

800

1000

Fig.1 Decomposition results of white noise after EMD

3 With the decomposition order increasing, the noise energy gradually decreases. That means that most noise interference is mainly assembled in high-order IMFs.

11 0.9

Normalized energy

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1

2

3

4

5

6

7

8

B. Energy variation characteristics of clutter in echo signal In short-range measuring, the main factor affecting the echo signal is the clutter interference. There may be a large number of clutter entering the receiver. In different background environments, the clutter spectrum is mainly distributed near the corresponding center frequency of the target and it is broadened sometimes. Thus, in order to study the variation characteristics of clutter energy in various IMFs, clutter signals in classic background environments (eg: lawn, sandy land and asphalt background) are collected. The test distances are set to 2.8m, 5.6m and 7.1m respectively. The related test conditions are described in Table 2.

IMF

Table 2 Conditions of clutter measurement Fig.2 Normalized energy of white noise

Parameters

From the Fig.2, it can be found that the energy of white noise decreases with the increase of IMF order, and the decreasing trend is approximately logarithmic. Most of the energy is concentrated on the first four orders. Starting from the fifth order IMF component, the energy of white noise is less than 10% of the initial energy and the value approximately tends to zero. In other words, white noise at low frequencies has little influence on useful information. Therefore, we assume that the order of IMF components containing most noise is determined by 10% of the initial energy. To justify the universality of the above assumption and results, 1000 times of Gauss white noise are generated randomly in Matlab software. Those noises are decomposed in turn by EMD and the energy of each order of IMF is calculated. The simulation results are presented in Fig 3. In 1000 simulation experiments, the results show that most of the energy of white noise is concentrated in the first three orders. From the fifth order IMF, it is generally less than 10% of the initial energy, which is basically consistent with the above conclusions.

Value

Transmitting power

8mW

Carrier frequency

24GHz

Modulated frequency

4KHz

Frequency deviation

560MHz

Scanning period

1ms

System gain

10

Antenna pattern

Forward

The collected data could not be calculated directly due to the CSV format. It is still necessary to process the data with the help of Matlab in order to carry out feature analysis. Firstly, the energy variation characteristics of the clutter IMF components under different background heights are compared. The normalized energy of each IMF component of the lawn, sand and asphalt background is pictured in Fig.4~Fig.6 respectively. 1 2.8m 5.6m 7.1m

0.9 0.8

Normalized energy

1 0.9

Normalized energy

0.8 0.7

0.7 0.6 0.5 0.4

0.6

0.3

0.5

0.2

0.4

0.1

0.3

0

2

3

4

5

6

7

8

Fig.4 Normalized energy of IMF in the background of lawn

0.1 0

1

IMF

0.2

1

2

3

4

5

6

7

IMF

Fig.3 Simulation results of white noise for 1000 times

8

4 1

1 2.8m 5.6m 7.1m

0.9 0.8

0.8 0.7 Normalized energy

Normalized energy

0.7 0.6 0.5 0.4 0.3

0.6 0.5 0.4

0.2

0.3

0.1

0.2

0

1

2

3

4

5

6

7

0.1

8

IMF

0

Fig.5 Normalized energy of IMF in the background of sand 1

0.8

1

2

3

4

5

6

7

8

IMF

Fig.7 Normalized energy of clutter in the background of lawn with different pitching angle

2.8m 5.6m 7.1m

0.9

1

0.7

0.9

0.6

0.8

0.5

0.7 Normalized energy

Normalized energy

20° 30° 40° 50° 60°

0.9

0.4 0.3 0.2 0.1

20° 30° 40° 50° 60°

0.6 0.5 0.4 0.3

0

1

2

3

4

5

6

7

8

0.2

IMF

Fig.6 Normalized energy of IMF in the background of asphalt

0

1

2

3

4

5

6

7

8

IMF

Fig.8 Normalized energy of clutter in the background of sand with different pitching angle 1 20° 30° 40° 50° 60°

0.9 0.8 0.7 Normalized energy

From the Fig.4~Fig.6, it can be observed apparently that the overall trend is similar in different altitudes and backgrounds although the variation of IMF energy is slightly different. When the critical energy is regarded as 10% of the initial energy, most of the energy in the lawn background appears in the first three-order IMF component and most of the energy in the sand and asphalt background is concentrated in the first four-order IMF component. Applying the same method, the clutter data at different elevation angles (20, 30, 40, 50 and 60 degrees) are measured at the same detection altitude. The clutter signals collected from different elevation angles are decomposed by EMD and the clutter energy in each IMF is calculated and normalized. Here, taking the detection height 7.1m as an example, the normalized energy of each order IMF component at different elevation angles is shown in Fig. 7 ~ Fig. 9. The results indicate that the energy variation at different angle is roughly the same as above conclusion. The main energy is still contained in the high-order IMF component. Starting from the fourth or the fifth order IMF, the energy of the clutter is generally lower than 10% of the initial energy.

0.1

0.6 0.5 0.4 0.3 0.2 0.1 0

1

2

3

4

5

6

7

IMF

Fig.9 Normalized energy of clutter in the background of asphalt with different pitching angle

8

5

0.03 IMF5 IMF6

0.025

0.03 IMF5 IMF6 0.025

Normalized energy

In particular, to further illustrate the variation characteristics of lower order IMFs, we set pitching angle 20 degree as an example to collect 20 groups data continually at different background environment due to the similarity of clutter energy variation rules at different angle. The normalized energy of fifth and sixth order IMFs under different background environment are presented in Fig.10~Fig.12, respectively.

0.02

0.015

0.01

Normalized energy

0.005

0.02 0

0.015

10 12 Data group

0.01

Fig. 12 Normalized energy of IMF5 and IMF6 in in the background of asphalt at 20°

0.005

0

2

4

6

8

10

12

14

16

18

20

Data group

Fig. 10 Normalized energy of IMF5 and IMF6 in the background of lawn at 20° 0.03 IMF5 IMF6

Normalized energy

0.025

0.02

0.015

0.01

0.005

0

2

4

6

8

10

12

14

16

18

20

Data group

Fig. 11 Normalized energy of IMF5 and IMF6 in the background of sand at 20°

2

4

6

8

14

16

18

20

From the Fig.10~Fig.12, it can be known that the clutter energy in the lawn, sandy land and asphalt background fluctuates about 2% of the initial energy in the fifth-order IMF while that is generally less than 1% in the sixth-order IMF. In fact, it is found in the experiment that the clutter energy after the sixth order tends to zero gradually. It means that the influence of clutter on lower order IMFs could be neglected. According to the above analysis, we can conclude that the energy of noise or clutter decreases gradually with decomposition. In the low order IMF, their influence has little effect on the expected signal. Therefore, the key to eliminate these disturbances is to find the proper order of IMF needed to filter. On the other hand, to improve the computational efficiency, it is not necessary to completely decompose the input frequency modulated signal to the residual signal. Considering that and combining with the previous measurement, we set the decomposition stopping time when the energy is lower than the 10% of the initial energy. In the subsequent filtering, the IMF components determined by the above condition are processed to eliminate the interference.

IV. MODULATION INTERVAL THRESHOLD FILTERING For the IMF components, if only the lower-order IMF components are preserved, the original signal is similar to be processed by the low-pass filter. If the higher-order IMF components are merely retained, that is same as the high-pass filtering. If only the middle IMF components are reserved, it is equivalent to bandpass filtering. The traditional EMD-based filtering method is to ascertain the IMF components dominated by noise firstly and then those IMFs are directly removed [15]. EMD-directly denoising (EMD-DD) method is simple to operate whereas it leads to the elimination of the target information contained in the high-order components at the same time. To improve the filtering effect, inspired by wavelet threshold filtering, Kopsinis. Y. et al. [16] proposed to adopt hard interval thresholding (HIT) and soft interval thresholding (SIT) to deal with the signals. The core of the two methods is to extract the necessary target information from the noise-dominated IMF components and to remove the noise

6 components from the target-dominated IMF components. The determination of the threshold Ti is based on the energy value of each IMF components:

Ti  0.7 Ei 2ln L

hard threshold or soft threshold directly eliminates the components within the upper and lower threshold, which could deform the useful signals. However, interval threshold can better preserve the integrity of waveforms [17,18]. Compared with HIT, SIT is smoother for signal processing, especially at the terminal points of the interval, which can avoid serious signal distortion [19]. The Fig. 13 presents the results of a noised sinusoidal signal (The amplitude is 1 and input SNR is 5dB.) processed by HIT and SIT, respectively. The direct processing results are shown in Fig 13(a). Meanwhile, the noised signal is also decomposed by EMD. One of the IMFs is used to be processed by HIT and SIT, respectively. Here, the IMF3 is taken as an example and the results are illustrated in Fig. 13(b). It can be found that the integrity and smoothness of the signal are kept well after SIT and the waveform is closer to the original pure signal. However, this performance is a little worse when processing the IMF components. In some local parts, the signal processed by HIT and SIT have been seriously deformed and the signal amplitude far exceeds the original signal.

(4)

Where, L is the sample length. The HIT and SIT can be expressed respectively as the follow: hi ( zij ), hi (ri j )  Ti  (5) hi ( zij )   j 0, h ( r )  T  i i i 

 hi (ri j )  Ti hi ( zij )( ), hi (ri j )  Ti hi (ri j ) (6) hi ( zij )    hi ( ri j )  Ti 0, Where, zij represents the interval of the j-th two adjacent zeros in an IMF component. hi (ri j ) is the extremum in the interval zij . hi ( zij ) depicts all sampling points in the interval.

hi ( zij ) is the component after threshold processing. Generally, 1.5 Pure Signal Noised Signal HIT SIT

1

Amplitude

0.5

-0.6

0

-0.8

-0.5

-1

-1

-1.2 1000

-1.5 0

200

400

600 Samples

800

1000

1060

1120

1180

1200

(a) IMF3 HIT SIT

Amplitude

0.05

0

-0.05 50

100

150 Samples

200

250

300

(b) Fig.13 Processing results of noisy sinusoidal signal

Furthermore, from the formula (5) and formula (6), we can notice that the difference between them is that a factor is additionally multiplied in SIT. The factor is dependent on the energy of the current IMF component and the signal extremum

in the interval. For every IMF component, the estimated energy Ti is pre-determined while the signal extremum is different in each interval. Especially for echo signals with clutter, the change of signal amplitude is often uncertain due to the randomness of clutter variation. In the adjacent interval, if the

7 difference between the two extremes is large and far greater than the threshold value, the whole signal in the interval will be eliminated after processing and some useful signals may be lost [20]. On the other hand, EMD is based on frequency band segmentation. For noise, the signal characteristics in each IMF after decomposition could not satisfy the simple Gauss distribution. At that time, HIT or SIT may not be suitable. Thus, in view of the characteristics of the echo signal and EMD, it is essential to adjust the SIT. An adaptive Modulation Interval Thresholding (AMIT) algorithm is proposed. The adjustment factor  is introduced into formula (6) in order to adjust the processing extent according to the extreme and threshold value. The specific expression is as the following:  hi (ri j )  Ti hi ( zij )( ), hi (ri j )  Ti j j h ( r ) (7) hi ( zi )   i i  j hi ( ri )  Ti 0, Where, the adjustment factor  is determined by the extreme and threshold value. The noise or clutter decomposed by EMD may not be processed by the formula (6) in the area of larger extremum or endpoint. Actually, when the extremum is large, the waveform in this area is often related to the useful signal [13]. Thus, the points near the extremum should be retained. In formula (6), the extremum points far greater than zero are directly eliminated and the extremum points closing to zero are reserved. Only relying on hi (ri j )  Ti could the processed signal cause exceeding the threshold locally. Considering that, two conditions should be satisfied with the threshold formula: 1) In an interval, from extreme to zero, the decrease of threshold should be inversely proportional to the amplitude of extreme value. 2) The thresholds in the interval with larger extremes should be lower than those with smaller extremes.

Therefore, we regard the hi (ri j ) / Ti as measurable criteria. The relationship between extreme value and threshold is regulated by the ratio of the criteria. At the same time, to facilitate calculation,  will be adjusted to an integer, namely:   hi (ri j ) / Ti  , hi (ri j ) / Ti is not integral   (8)    j j h ( r ) / T  1, h ( r ) / T is integral  i i i i  i i Where, [] denotes following integral function. It means the

hi (ri j ) / Ti should be integral value and must be rounded down. From the formula (7) and (8), it can be observed that the decrease of threshold is regulated by  . When the extreme in an interval is large, the  is also large. The threshold calculated by the formula (7) is small, which obviously satisfies the above two conditions. Next, we take the sinusoidal signal as an example to illustrate the rationality of adjustment factor. Fig. 14 gives the results of a sinusoidal signal processed by SIT and AMIT, respectively. Signal 1 and Signal 2 have the same amplitude (both amplitudes are 1) while different threshold processing is adopted (the threshold of Signal 1 is set to 0.8 and the threshold of Signal 2 is set to 0.5). Signal 1 and 3 have different amplitudes (the amplitude of Signal 3 is set to 2) while both of them are processed by the same threshold (threshold is set to 0.8). For signals with the same amplitude, the signal components are less removed when the threshold is low. For signals with different amplitudes, when the same threshold is adopted, the higher the amplitude, the less the signal components will be eliminated. Most of the Signal 3 is retained because the local extremum of Signal 3 is large. In Fig. 14, no matter what the signal amplitude or threshold is set, the characteristics of the signal can be retained better in the method of AMIT. AMIT not only owns the advantages of SIT, but also makes the signal processing more flexible.

1.5

1.5 Signal1

SIT

2 Signal2

AMIT

1

1

0.5

0.5

0

0

-0.5

-0.5

SIT

AMIT

SIT

AMIT

1

Upper threshold

Amplitude

Signal3

1.5

0.5 0 -0.5 -1

Lower threshold

-1 -1.5

0

200

400

600 800 Samples

1000

-1 -1.5 0 1200

-1.5 200

400

600 800 Samples

1000

1200

-2

0

200

400

600 800 Samples

1000

1200

Fig. 14 Results of sinusoidal signals after SIT and AMIT processing

V. VERIFICATION In previous sections, the principle of EMD and AMIT are stated. To further evaluate the performance of the proposed method and compare to other methods, the simulation and practical test are conducted. The signals are processed by above mentioned methods, namely, EMD-DD、EMD-HIT、EMD-SIT

and EMD-AMIT. The processing flowchart of the four methods is shown in Fig. 15. First of all, the typical test signals (namely ‘Bump’，‘Doppler’ and ‘Blocks’) are simulated. The three kinds of the test signal are presented in Fig. 16. The ‘Bump’ signal, ‘Doppler’ signal and ‘Blocks’ signal with different SNR are generated by Matlab. The signal length is 1000 sampling points. The input SNR varies from 1dB to 9dB in steps of 2dB. Output SNR (OSNR)

8 and root mean square error (RMSE) are used as evaluation criteria. Input signal s

Decompose s by EMD

Decompose s by EMD until the energy of IMF is lower than 10% of the initial energy

Find IMFs dominated by noise

Filter higher-order IMFs by HIT

Filter higher-order IMFs by SIT

Filter IMFs by AMIT

Eliminate noised IMFs and reconstruct residuals

Reconstruct processed IMFs and residuals

Reconstruct processed IMFs and residuals

Reconstruct all processed IMFs

EMD-SIT

EMD-AMIT

EMD-DD

EMD-HIT

Fig.15 Flow chart of the four algorithms

5

Doppler

0

Amplitude

5 0 OSNR=10.9590dB

-5 10

EMD-HIT

5 0 OSNR=7.2313dB EMD-SIT

5 0 OSNR=12.9592dB

-5 10

10

Amplitude

-5

Amplitude

Pure signal EMD-DD

-5 10

0

Blocks

5 0

-5

0 Noised signal(SNR=5dB)

Amplitude

5

-5 10 Amplitude

Bumps

5

-5 10

Amplitude

Amplitude

10

Amplitude

10

The calculation of RMSE is as the follow: 1 N (9) RMSE   ( x(n)  x(n))2 N n 1 Where, x(n) and x(n) are original sequence and output sequence, respectively. Usually, the RMSE is employed to compute the error of the processed component with the real component. Less RMSE value means a more accurate component. Taking the results of ‘Bump’ signal (ISNR=5dB) as an example to illustrate the effect of the four methods. The results are shown in Fig. 17. The SNR results of ‘Bump’ signal, ‘Doppler’ signal and ‘Block’ signal after filtering are shown in Table 3. The RMSE of three signals is described in Fig. 18, Fig. 19 and Fig. 20.

EMDAMIT

5 0 OSNR=14.0170dB

-5 0

200

400

600 Samples

800

1000

Fig. 16 Three kinds of test signal (The black line is pure signal and the red line is noised signal)

0

200

400 600 Samples

800

1000

Fig. 17 Comparison of filtering for Bumps signal (ISNR=5dB) in four algorithms

9 0.65

Table 3 SNR after filtering for three signals

1

3

5

7

9

0.6

Signal

EMD-DD

EMD-HIT

EMD-SIT

EMD-AMIT

Bumps Doppler Blocks Bumps Doppler Blocks Bumps Doppler Blocks Bumps Doppler Blocks Bumps Doppler Blocks

3.8897 3.8976 3.5166 8.4106 8.4245 8.3709 10.9590 10.5630 10.2820 11.2623 11.5969 11.3824 13.8869 13.8242 12.1746

1.3524 1.4615 1.3047 5.4445 5.0785 4.9937 7.2313 7.7091 6.9641 8.9698 8.5290 8.6616 9.5952 9.9607 9.9907

6.0523 6.1909 6.0443 10.6863 10.4190 10.1166 12.9592 12.8663 11.6387 12.8749 13.1448 12.5562 13.2834 14.7897 13.6257

8.0164 7.3853 7.3171 11.7653 11.1266 11.6398 14.0170 13.2981 12.5473 13.8824 14.1120 13.8559 15.1082 15.9385 14.7800

EMD-DD EMD-HIT EMD-SIT EMD-AMIT

0.55 0.5 0.45

RMSE

ISNR (dB)

0.4 0.35 0.3 0.25 0.2 1

2

3

4

5 6 ISNR/(dB)

7

8

9

Fig. 19 RMSE of Doppler signal 0.65

0.65 0.6

EMD-DD EMD-HIT EMD-SIT EMD-AMIT

0.55

0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2

1

2

3

4

5 6 ISNR/(dB)

7

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Fig. 20 RMSE of Blocks signal The proposed method is merely compared with EMD-SIT because the previous simulation indicates that the EMD-SIT has advantages over other traditional algorithms in the aspect of denoising. The ideal condition echo and the practical collected signals from the background of lawn, sand and asphalt are shown in Fig. 21(a) ~Fig. 21(d), respectively. The basic measurement conditions are same as the Table 2. The detect distance is also the same (7.1m) at the three cases. The original signals still need to accomplish the format conversion by the use of Matlab. In Fig. 21, the left part is the signals in the time domain and the corresponding frequency spectrum on the right.

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(d) Asphalt background Fig. 21 The collected signals and frequency spectrum From the frequency spectrum, it is hard to recognize the real peak frequency that represents the distance from the detector to the ground. There are also abundant interference in the echo signal. The above three signals are processed by the EMD-SIT and EMD-AMIT, respectively. The results are depicted in Fig. 22. The results show clearly that both the two methods facilitate the recognition of the desired signal. For EMD-AMIT, the effectiveness of denoising is obviously better than EMD-SIT. The expected frequency varies from other interference and is convenient to be measured. By means of calculation, the SNR after EMD-SIT in the three cases are 9.88dB, 10.23dB, 11.30dB while that is improved to 11.36dB, 13.57dB and 14.98dB after EMD-AMIT, respectively. The improvement of SNR means that the measurement of expected frequency can be obtained more accurately. In other words, the corresponding precision of detection range can be improved.

Aiming at the characteristics of echo signal in frequency modulated system, an adaptive interval denoising algorithm based on EMD is proposed in this paper. Through a lot of experiments, the characteristics of noise and clutter energy varying with the order of IMF in the echo signal are analyzed. Most of the energy of noise and clutter is concentrated in the high-order IMF components. To improve the efficiency of processing, it is not necessary to decompose sequentially when the energy of IMF component is lower than the 10% of the initial energy. The denoising performance of EMD-AMIT is validated by three typical test signals and real echo signals. The results show that the proposed algorithm has obvious effect on improving SNR and reducing RMSE. In the future, we will continue to do further research on the real-time decomposition of EMD and the effective extraction of target signals in order to reduce signal processing delay and meet the requirements of higher accuracy of real-time measurement.

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